The Short answer is No. Ubuntu was patched on 7th April 2014 and the bug was widely reported on 8th April, 2014. If you are using other operating systems, you need to worry. Especially if its non-Linux based.

The Heartbleed vulnerability that was discovered just last week took the world by surprise, but most of the affected services and operating systems have been patched. Unfortunately, some of the Ubuntu users haven’t understood how the patching process works and have started to flood the forums and other social media with the message that Ubuntu is vulnerable.

Before the OpenSSL issues has become known to the general public, most of the Linux distributions affected by the issue were patched. Most of the media reported on the problem on April 8, but the patch for the Heartbleed vulnerability was already in place on April 7. This is how the security notification looks like in Ubuntu.